Schematic representation of two typical surface hopping trajectories (red and green dashed lines). At any moment in time the system is propagated in a pure electronic quantum state, but transitions between different electronic states are allowed. The probability for a nonadiabatic surface switch depends on the strength of the nonadiabatic coupling. Small energy gaps between two states generally result in high transition probabilities. Surface hops, therefore, tend to occur mainly in the vicinity of (avoided) surface crossings.

Chemical reactions rarely take place spontaneously; energy generally needs to be supplied in order to activate them. In the case of thermal reactions an activation barrier in the electronic ground state is overcome by heating the system. Photoreactions, on the other hand, only occur upon absorption of light promoting an electron into an excited state. Often the excited state dynamics is not entirely independent of the ground state (or other excited states), i.e. the two (or more) electronic states are coupled. In such a scenario one speaks of nonadiabatic dynamics.

Theoretical treatment of nonadiabatic dynamics requires two main ingredients, a reliable method to calculate excited states and a technique to perform molecular dynamics (MD) simulations in two or more coupled electronic states. Car-Parrinello (or ab initio) molecular dynamics (CP-MD) is a technique to simultaneously propagate atomic nuclei and their electrons based on density functional theory (DFT). Until recently this method was applicable only to systems in the electronic ground state. In 1998, a novel CP-MD scheme was introduced that made possible MD simulations in the lowest excited singlet state, S₁. We have combined the ground and excited state CP-MD approaches and, in addition, incorporated nonadiabatic effects by implementing a so-called surface hopping algorithm (see Fig. 1). Our nonadiabatic CP-MD (na-CP-MD) method has been tested on a well-known photochemical reaction in the gas phase, namely the cis-trans photoisomerisation of formaldimine (see Fig. 2). Photoisomerisation about a double bond plays an important role in many biological processes such as vision. However, since real-life biochemical reactions usually take place in aqueous solution, it is desirable to be able to carry out nonadiabatic MD simulations of condensed phases. This is where the present na-CP-MD approach is most efficient. In order to demonstrate the applicability of na-CP-MD to condensed phase systems, we have studied the trans-cis photoisomerisation of diazene, N₂H₂, in aqueous solution (see Fig.3).

Schematic view of the photoreaction pathways of formaldimine (R1=R2=H). S₀ (red) and S₁ (blue) energy curves are plotted qualitatively against a hypothetical reaction coordinate whose main contributor is the NH twist angle (defined here as the angle between the planes containing R₁CR₂ and HNC, respectively). Upon irradiation of the planar reactant R with light, the molecule is lifted vertically into the S₁ state where it moves down the potential slope. As the excited state energy decreases, the NH twist angle approaches 90^o, at which point the S₀ and S₁ potential surfaces cross. Near this surface crossing, nonadiabatic coupling is strong and a transition back to the ground state occurs. Two reaction branches are now possible: if the system falls down to the left (R), no isomerisation has taken place; if it falls down to the right, the photoproduct P is formed.

Photoisomerisation of diazene, N₂H₂, in aqueous solution. The simulation was carried out in a periodically repeated unit cell containing 30 water molecules at room temperature. At the start of the calculation, the trans isomer of diazene is photoexcited. Similar to the case of formaldimine which is depicted in Fig. 2, one of the NH bonds begins to twist out of plane and finally flips to the other side of the NN axis forming the cis isomer.